baseball - game played between two teams of nine players each who take turns batting and fielding2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than
2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're given two equations: [LIST=1] [*]a = 2b + 3 [*]a + b = 60 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: 2b + 3 + b = 60 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get: b = [B]19 [/B] To solve for a, we substitute b = 19 into equation (1): a = 2(19) + 3 a = 38 + 3 a = [B]41[/B]
2000 people attended a baseball game 1300 of the people attending supported the home team while 700 supported the visiting team what percentage of people attending supported the home team We want the percentage of 1300 out of 2000. [URL='https://www.mathcelebrity.com/perc.php?num=1300&den=2000&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We go to our search engine and type 1300 out of 2300 as a percent[/URL] and we get: [B]65%[/B]
A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]
a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ? 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ? 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ? 252.4.5 [B]t ? 56[/B]
A baseball player gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits? Percent Hits = 12/40 Using our [URL='http://www.mathcelebrity.com/perc.php?num=12&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percent calculator[/URL], we get [B]30%[/B] Since you either get a hit or you don't, we subtract 30% from 100% to find the percent of not hits: Percent Not Hits = 100 - 30% = [B]70%[/B]
A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? We set up a proportion of hits to games where h is the number of hits the player gets in 45 games: 3/15 = h/45 [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].
A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? Let's find the proportion of hits to games. Using h as the number of hits in 45 games, we have: 7/15 = h/45 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get h = 21
a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400? Let the amount of consecutive hits needed be h. We have: hits / at bats = Batting Average Plugging in our numbers, we get: (9 + h)/60 = 0.400 Cross multiply: 9 + h = 60 * 0.4 9 + h = 24 To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get: h = [B]15[/B]
A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last. (This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.) First 8 positions: [URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200 For the pitcher, we can have 10 different possibilities for the 9th player: 259,459,200 x 10 = [B]2,594,592,000 ways[/B]
A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win? Using our percentage calculators, we type the following statements into our search engine and get: [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39 For a total of 52.5 games won The team played 30 + 60 = 90 games. So we want to know the pecent: [URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']52/90[/URL] = [B]57.78%[/B]
a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X. We have: [B]y = 21x + 5[/B] Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family. We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.
Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3577.00 for 1197 paid admissions. How many of each ticket were sold? Let g be the number of tickets for general admission Let r be the number of tickets for reserved seats We have two equations: [LIST=1] [*]g + r = 1197 [*]2g + 5.50r = 3577 [/LIST] We can solve this a few ways, but let's use substitution using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=g+%2B+r+%3D+1197&term2=2g+%2B+5.50r+%3D+3577&pl=Substitution']simultaneous equations calculator[/URL]: [LIST] [*][B]r = 338[/B] [*][B]g = 859[/B] [/LIST]
At Billys Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower seeds, $1.50, and cleats $85.00. Write an expression if you bought b bats, s sunflower seeds, and c cleats. Since amount = cost * quantity, we have a cost of: [B]45b + 1.50s + 85c[/B]
Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: [LIST=1] [*]Benny buys 8 new cards, so we add 8 to get b + 8 [*]The dog ate half of his cards the next day, so Benny has (b + 8)/2 [*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47 [/LIST] (b + 8)/2 = 47 [B][U]Cross multiply:[/U][/B] b + 8 = 47 * 2 b + 8 = 94 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].
Carter is going away to college and is giving his collection of 531 baseball cards to his cousins. If he gives 227 cards to Lewis, 186 cards to Benny, and 18 cards to Seven, how many cards are left over? When Carter gives away cards, he subtracts from his collection. So we have: 531 - 227 - 186 - 18 = [B]100 cards leftover[/B]
Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to? Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations: [LIST=1] [*]6f + 5 = n [*]8f - 7 = n [/LIST] Since both equations equal n, we set these equations equal to each other 6f + 5 = 8f - 7 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get: f = [B]6 [/B] To check our work, we plug in f = 6 into each equation: [LIST=1] [*]6(6) + 5 = 36 + 5 = 41 [*]8(6) - 7 = 48 - 7 = 41 [/LIST] So this checks out. Clark has 41 total cards which he gives to 6 friends.
Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with? Let the starting amount of cards be s. We're given: [LIST] [*]Dan bought 7 new cards: s + 7 [*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2 [*]Now, he's got 26 cards left. So we set up the following equation: [/LIST] (s + 7)/2 = 26 Cross multiply: s + 7 = 26 * 2 s + 7 = 52 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get: s = [B]45[/B]
Dan bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 30 cards left. How many cards did Dan start with? Let the original collection count of cards be b. So we have (b + 8)/2 = 30 Cross multiply: b + 8 = 30 * 2 b + 8 = 60 [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B8%3D60&pl=Solve']Use the equation calculator[/URL] [B]b = 52 cards[/B]
George has 600 baseball cards and Joy has one fifth as many baseball cards as George. How many baseball cards does joy have? Let j = Joy's cards and g = George's cards. We have the following equation: g = 600 j = 1/5g So j = 600/5 [B]j = 120[/B]
Hayden bought 48 new trading cards. Three-fourths of the new cards are baseball cards. How many baseball cards did Hayden buy? We want 3/4 of 48. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=48&frac2=3/4&pl=Multiply']type this statement into our calculator[/URL] and we get: [B]36[/B]
How many possible batting orders are there for a baseball team with 9 players? 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = [B]362,880 batting orders[/B]
In 1 year, a baseball player got 195 hits in 600 times. What is his batting average? Batting Average = Hits / Times at Bat Batting Average = 195 / 600 [URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Batting Average[/URL] = [B]0.327[/B]
In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have: b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already [/I] We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get: b = [B]6[/B]
mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow? P(yellow) = yellow caps / Total caps P(yellow) = 12/(12 + 18) P(yellow) = 12/30 [URL='https://www.mathcelebrity.com/fraction.php?frac1=12.%2F30&frac2=3%2F8&pl=Simplify']Simplifying this fraction,[/URL] we get: P(yellow) = [B]2/5[/B]
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)
b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of the average of 49 fly balls a. N(250, 50/sqrt(49)) = [B]0.42074[/B] b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL] c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL] Using the Z-score formula, we have 0.8416 = (x - 250)/50 x = [B]292.08[/B]
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. a. If X = distance in feet for a fly ball, then X ~ b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement. a. [B]N(250, 50/sqrt(1))[/B] b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL] Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B] c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL] Z-score formula: 0.8416 = (x - 250)/50
x = [B]292.08[/B]
The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs for $10 each. How much more did the basketball coach spend than the baseball coach? [U]Baseball coach spend:[/U] Spend = Number of baseballs * cost per baseball Spend= 2 * $1 Spend = $2 [U]Basketball coach spend:[/U] Spend = Number of basketballs * cost per basketball Spend= 7 * $10 Spend = $70 [U]Calculate the difference in spend:[/U] Difference = Basketball coach spend - Baseball coach spend Difference= $70 - $2 Difference= [B]$68[/B]
the basketball coach bought 8 new basketballs for 2$ each. the baseball coach bought 8 new baseballs for 25$ each. how much more did the basketball coach spend than the baseball coach. [LIST] [*]Basketball Coach Spend: 8 basketballs * $2 = $16 [*]Baseball Coach Spend: 8 baseballs * $25 = $200 [/LIST] The Baseball Coach spent $200 - $16 = [B]$184[/B] more than the Basketball coach
The price of a baseball glove is no more than $38.95. Let p be the price of the baseball glove. The phrase "no more than" means less than or equal to. Our inequality is: p <= $38.95
There are 377 baseball teams at the tournament and each team has 228 players. How many players are at the tournament? Key words are "There are", "each team", and "how many". We multiply teams by players per team to get number of players. 377 * 228 = [B]85,956[/B]
Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the total number of baseball cards he has now. 144 and m more means we add [B]144 + m[/B]
Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the total number of baseball cards he has now. 9 more means we add 9 to n [B]n + 9[/B]
ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfqLKivsKhZamgoHS%2Bfq7ArJybmZyh